SOLUTION: Q) Find dy/dx for each of the following. a) y=-1/6(e^(-3x))+x(2x-1) b) 3x^(2)y-xy^2=sin^(2)3x

Algebra ->  Circles -> SOLUTION: Q) Find dy/dx for each of the following. a) y=-1/6(e^(-3x))+x(2x-1) b) 3x^(2)y-xy^2=sin^(2)3x      Log On


   

Question 1067104: Q) Find dy/dx for each of the following.
a) y=-1/6(e^(-3x))+x(2x-1)
b) 3x^(2)y-xy^2=sin^(2)3x
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y=-1/6(e^(-3x))+x(2x-1); second term is 2x^2-x
y'=(1/2)(e^(-3x))+4x-1
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3x^2(dy/dx)+6xy-2xy(dy/dx)-y^2=2 sin (3x)*cos(3x)*3
[3x2-2xy] (dy/dx)+6xy-y^2=6 sin(3x)(cos(3x))
dy/dx=[6 sin (3x)*cos (3x)+y^2-6xy]/(3x^2-2xy)
Note: 6 sin (3x)(cos(3x)=3sin (6x), because sin (2a)=2 sin (a) cos (a)